Question: Solve for $x$ and $y$ using elimination. $\begin{align*}2x-6y &= -1 \\ 3x+6y &= -6\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $5x = -7$ Divide both sides by $5$ and reduce as necessary. $x = -\dfrac{7}{5}$ Substitute $-\dfrac{7}{5}$ for $x$ in the top equation. $2( -\dfrac{7}{5})-6y = -1$ $-\dfrac{14}{5}-6y = -1$ $-6y = \dfrac{9}{5}$ $y = -\dfrac{3}{10}$ The solution is $\enspace x = -\dfrac{7}{5}, \enspace y = -\dfrac{3}{10}$.